Improved Simulation of Stabilizer Circuits

The Gottesman-Knill theorem says that a stabilizer circuit -- that is, a quantum circuit consisting solely of CNOT, Hadamard, and phase gates -- can be simulated efficiently on a classical computer. This paper improves that theorem in several directions. First, by removing the need for Gaussian elimination, we make the simulation algorithm much faster at the cost of a factor-2 increase in the number of bits needed to represent a state. We have implemented the improved algorithm in a freely-available program called CHP (CNOT-Hadamard-Phase), which can handle thousands of qubits easily. Second, we show that the problem of simulating stabilizer circuits is complete for the classical complexity class ParityL, which means that stabilizer circuits are probably not even universal for classical computation. Third, we give efficient algorithms for computing the inner product between two stabilizer states, putting any n-qubit stabilizer circuit into a "canonical form" that requires at most O(n^2/log n) gates, and other useful tasks. Fourth, we extend our simulation algorithm to circuits acting on mixed states, circuits containing a limited number of non-stabilizer gates, and circuits acting on general tensor-product initial states but containing only a limited number of measurements.Comment: 15 pages. Final version with some minor updates and corrections. Software at http://www.scottaaronson.com/ch

Synthesis and Optimization of Reversible Circuits - A Survey

Reversible logic circuits have been historically motivated by theoretical research in low-power electronics as well as practical improvement of bit-manipulation transforms in cryptography and computer graphics. Recently, reversible circuits have attracted interest as components of quantum algorithms, as well as in photonic and nano-computing technologies where some switching devices offer no signal gain. Research in generating reversible logic distinguishes between circuit synthesis, post-synthesis optimization, and technology mapping. In this survey, we review algorithmic paradigms --- search-based, cycle-based, transformation-based, and BDD-based --- as well as specific algorithms for reversible synthesis, both exact and heuristic. We conclude the survey by outlining key open challenges in synthesis of reversible and quantum logic, as well as most common misconceptions.Comment: 34 pages, 15 figures, 2 table

Quantum walks: a comprehensive review

Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists, mathematicians and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing Journa

There is more than one way to turn a spherical cellular monolayer inside out: type B embryo inversion in Volvox globator

Höhn S, Hallmann A. There is more than one way to turn a spherical cellular monolayer inside out: type B embryo inversion in Volvox globator. BMC Biology. 2011;9(1): 89.Background: Epithelial folding is a common morphogenetic process during the development of multicellular organisms. In metazoans, the biological and biomechanical processes that underlie such three-dimensional (3D) developmental events are usually complex and difficult to investigate. Spheroidal green algae of the genus Volvox are uniquely suited as model systems for studying the basic principles of epithelial folding. Volvox embryos begin life inside out and then must turn their spherical cell monolayer outside in to achieve their adult configuration; this process is called 'inversion.' There are two fundamentally different sequences of inversion processes in Volvocaceae: type A and type B. Type A inversion is well studied, but not much is known about type B inversion. How does the embryo of a typical type B inverter, V. globator, turn itself inside out? Results: In this study, we investigated the type B inversion of V. globator embryos and focused on the major movement patterns of the cellular monolayer, cell shape changes and changes in the localization of cytoplasmic bridges (CBs) connecting the cells. Isolated intact, sectioned and fragmented embryos were analyzed throughout the inversion process using light microscopy, confocal laser scanning microscopy, scanning electron microscopy and transmission electron microscopy techniques. We generated 3D models of the identified cell shapes, including the localizations of CBs. We show how concerted cell-shape changes and concerted changes in the position of cells relative to the CB system cause cell layer movements and turn the spherical cell monolayer inside out. The type B inversion of V. globator is compared to the type A inversion in V. carteri. Conclusions: Concerted, spatially and temporally coordinated changes in cellular shapes in conjunction with concerted migration of cells relative to the CB system are the causes of type B inversion in V. globator. Despite significant similarities between type A and type B inverters, differences exist in almost all details of the inversion process, suggesting analogous inversion processes that arose through parallel evolution. Based on our results and due to the cellular biomechanical implications of the involved tensile and compressive forces, we developed a global mechanistic scenario that predicts epithelial folding during embryonic inversion in V. globator

What Is the Evidence to Support the Use of Therapeutic Gardens for the Elderly?

Horticulture therapy employs plants and gardening activities in therapeutic and rehabilitation activities and could be utilized to improve the quality of life of the worldwide aging population, possibly reducing costs for long-term, assisted living and dementia unit residents. Preliminary studies have reported the benefits of horticultural therapy and garden settings in reduction of pain, improvement in attention, lessening of stress, modulation of agitation, lowering of as needed medications, antipsychotics and reduction of falls. This is especially relevant for both the United States and the Republic of Korea since aging is occurring at an unprecedented rate, with Korea experiencing some of the world's greatest increases in elderly populations. In support of the role of nature as a therapeutic modality in geriatrics, most of the existing studies of garden settings have utilized views of nature or indoor plants with sparse studies employing therapeutic gardens and rehabilitation greenhouses. With few controlled clinical trials demonstrating the positive or negative effects of the use of garden settings for the rehabilitation of the aging populations, a more vigorous quantitative analysis of the benefits is long overdue. This literature review presents the data supporting future studies of the effects of natural settings for the long term care and rehabilitation of the elderly having the medical and mental health problems frequently occurring with aging